Great question, thanks for asking it here! You only need a storage volume if you need to add storage to your droplet, or have a detachable storage volume that you can move between droplets (like a USB drive). For deploying a Laravel app, I recommend using this tutorial as a guide:

Ubuntu 18 is not much different from 16 in most steps, but you may have to find out how to do something specific to 18 if you run into any particular step that fails (if anything it would probably be package names that contain version numbers).

Now one thing to note, you already have Apache+PHP installed on this droplet, so you’re editing an existing environment. This tutorial is minimal and may have to be adjusted to your needs, but it looks pretty solid to me for your situation.